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MATH 16A, SUMMER 2008, REVIEW SHEET FOR FINAL EXAM
BENJAMIN JOHNSON
The ﬁnal exam will be held Thursday, August 14, from 8:10AM to 10:00AM in 3 Evans. The
exam will be cumulative, but will focus more on chapters 3, 4, 5, and 6 of the textbook.
To do well on this exam you should be able to answer any simple question related to the essential
ideas in calculus, including some material covered in chapters 02 (such as taking the derivative of
a function). You can assume that any material on the exam will be either recent material from
chapters 36; or material that has been covered extensively, used consistently since its introduction
in the course, and appeared at least once on a previous quiz, midterm, or midterm review sheet.
Consult your previous midterm review sheets, midterm solutions, and quiz solutions for highlights of
material from earlier chapters. At least 60% (and probably more) of the exam will focus exclusively
on material covered since the midterm exam. In relation to that material, you should be able to do
at least each of the following:
Chapter 3. TECHNIQUES OF DIFFERENTIATION
3.1 The Product and Quotient Rules
(1) State the product rule and the quotient rule.
(2) Use the product rule or quotient rule to diﬀerentiate functions [such as
f
(
x
) =
(
x
2
+ 1)(
x
3
+ 2
x
+ 3) or
g
(
x
) =
x
2

1
3
x
2
+2
].
3.2 The Chain Rule and the General Power Rule
(1) Express a function as a composition of two functions. [For example, if
h
(
x
) =
(
x
+2
3
x
)
4
, ﬁnd
f
and
g
such that
h
=
f
◦
g
].
(2) State the chain rule using either Newton’s notation or Leibniz’ notation.
(3) Use the chain rule to compute the derivative of a function (such as
y
= (
x
2
+1)
2
).
3.3 Implicit Diﬀerentiation and Related Rates
(1) Use implicit diﬀerentiation to ﬁnd the slope of the tangent line to a curve (when
the curve is not expressed as a function). [For example, ﬁnd the slope of the
tangent to the curve
x
2
+
y
2
= 4 at the point (1
,

√
3)].
(2) Use implicit diﬀerentiation to ﬁnd
dy
dx
,
dx
dy
,
dy
dt
, or
dx
dt
given an equation relating
x
and
y
[such as
y
+ 2
x
+
xy
= 38]. Answer a similar question if the letters are
something other than
x
,
y
, and
t
.
(3) Solve an application problem involving related rates. [For example, if a 10 foot
ladder is sliding down a wall at a rate of 4 feet per second, how fast is the ladder
moving along the ground when the ladder is 5 feet from the ground?]
Chapter 4. THE EXPONENTIAL AND NATURAL LOGARITHM FUNCTIONS
4.1 Exponential Functions
(1) Use properties of exponents to simplify expressions involving exponents. [For
example, write (2
4
x
·
2

x
)
1
2
in the form 2
kx
for some constant
k
.]
(2) Solve for
x
an equation in which
x
occurs as an exponent, [for example, 27 = 3
5
x
].
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This note was uploaded on 05/12/2010 for the course CHEM 3A taught by Professor Fretchet during the Fall '08 term at University of California, Berkeley.
 Fall '08
 Fretchet

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